There is no standard amount or numbers. What you're referring to here is having someone invest in the GP entity. First, you need to set a valuation on the GP entity. A good place to start is by trying to pencil out the value of the carry if you 3x the fund. Then, you can work backward to determine how much $ a % of the GP is worth. 

This transaction is typically not contingent on fundraising targets. Instead, an investor will buy a portion of your carry for a set amount, similar to how you would invest in a startup. If the fund fails, the investment in the GP goes to 0. 

It is not very advantageous for investors to invest in the GP because they get paid last. The best place for investors to invest is the LP entity, because there they get paid first. Therefore, those who chose to invest in the GP vs the LP entity often do so because a) they want to help the manager and b) they want to get better economics on their initial LP investment.